This year, there was her snappy, unapologetic Sylvia in the Tom Stoppard HBO miniseries “Parade’s End,” a revelation of Hall’s dynamism and capacity for boldness. There was her supporting role as a scientist in “Iron Man 3,” an indoctrination to the Hollywood blockbuster. And, now, there’s the British thriller “Closed Circuit,” a confirmation of her ascendance to being a leading lady — one bristling with intelligence in any role.

“I want to play women who are rich and make mistakes and can be messy and ugly as well as pretty,” says Hall. “I think that’s really an important service. That sounds very grand. I don’t mean it to sound grand.”

In a recent interview over tea at an East Village cafe, Hall is sharp, buoyant, funny and seemingly energized by the work she’s getting. She’s still glowing from the singing lines of Sylvia — a “once in a blue moon” part, she calls it — a shift for her to playing a more extroverted, forceful character: “It was massively liberating,” she says.

Above all, she comes across, as she says of herself, as “restless and curious.”

“She’s the real McCoy,” says “Closed Circuit” director John Crowley. “She’s hugely impressive and has massive range. It felt like she would have the intellectual prowess but also the emotionality to handle the part.”

In “Closed Circuit,” Hall plays the Special Advocate appointed to jointly defend a man accused of bombing a crowded London marketplace. She and another lawyer (Eric Bana), with whom she has a romantic past, must work the case under confidentiality and in a hearing closed to the public — a cloak of secrecy that masks further injustice in the name of national security.

The film has obvious contemporary relevance, but it also relates personally to Hall. The 31-year-old actress has seen her life made the fodder of British tabloids for her relationship with director Sam Mendes.

“I find it slightly disturbing that privacy means that you’re guilty of something that you have to hide,” Halls says. “That probably stems from the fact that I saw my parents have their privacy invaded on by the press when they were going through their divorce when I was five or whatever. I was very aware of the press always — my dad’s reviews.”

Hall’s father, Sir Peter Hall, founded the Royal Shakespeare Company and is a renowned figure in British theater. Her mother, Maria Ewing, was an acclaimed opera singer from Detroit.

Of her childhood, Hall says: “It was mine. I don’t know any different. It was peripatetic and nomadic and bohemian and exciting and at times unusual to the point of wanting some type of stability. But mostly, it was just a very creative, exciting environment to be raised in.”

As a child, Hall was immediately drawn to acting: Her first professional part came as an 8-year-old in her father’s TV adaptation of Mary Wesley’s “The Camomile Lawn.” She later attended Cambridge for two years, but then quit, wanting “to do something bold and decisive and not have anything to fall back on.”

With such an independent streak, she initially recoiled when her father offered her a part in his production of George Bernard Shaw’s “Mrs. Warren’s Profession” in the West End.

“Then I changed my mind after six months and realized I might as well get it out of the way,” she recalled. “Either I’ll be mauled by the press and I’ll never be allowed to do this again, or they’ll get over the fact that I’m Peter Hall’s daughter.”

Hall won the Ian Charleson Award for the performance. Years of theater and frequent collaborations with her father followed. She stared in Mendes’ Bridge Project, productions of “The Winter’s Tale” and “The Cherry Orchard.”

Her approach to a part — a process she’s somewhat protective of — is carefully plotted. She papers the walls of her trailer with charts of her characters’ mental states, scene to scene. She laughs that she had “a complete and utter meltdown” when her blueprints were temporarily cleaned away while recently filming the science-fiction thriller “Transcendence,” co-starring Johnny Depp.

Hall also makes playlists for every character of what she thinks they would listen to as a key to their emotions, (contemporary classical and Scandinavian jazz trios for her passionate but suppressed character in “Closed Circuit”).

“Of all the actresses I’ve ever worked with, she was the most clear, the most thought-out,” says Susanna White, director of “Parade’s End.” ”She’d come in and kick it straight away. It was thrilling to watch.”

This December, Hall will make her Broadway debut in “Machinal,” an expressionistic 1928 play based on Ruth Snyder, who was convicted of murdering her husband. Describing the character, Hall drifts into contemplation: the early wheels turning on the next character to map out.